Managing structural uncertainty in health economic decision models: a discrepancy approach

Healthcare resource allocation decisions are commonly informed by computer model predictions of population mean costs and health effects. It is common to quantify the uncertainty in the prediction due to uncertain model inputs, but methods for quantifying uncertainty due to inadequacies in model structure are less well developed. We introduce an example of a model that aims to predict the costs and health effects of a physical activity promoting intervention. Our goal is to develop a framework in which we can manage our uncertainty about the costs and health effects due to deficiencies in the model structure. We describe the concept of `model discrepancy': the difference between the model evaluated at its true inputs, and the true costs and health effects. We then propose a method for quantifying discrepancy based on decomposing the cost-effectiveness model into a series of sub-functions, and considering potential error at each sub-function. We use a variance based sensitivity analysis to locate important sources of discrepancy within the model in order to guide model refinement. The resulting improved model is judged to contain less structural error, and the distribution on the model output better reflects our true uncertainty about the costs and effects of the intervention.